Some good L-fuzzy compactness-related concepts and their properties, I

On characterizations of some covering properties in L-fuzzy topological spaces in Šostak's sense

“…If g is the whole space X , we say that the L-fts ðX ; TÞ is almost compact (respectively, nearly compact). In the crisp case of T, almost compactness (respectively, near compactness) coincides with the almost compactness (respectively, near compactness) introduced by Kudri and Warner [16].…”

The semi-precompactness axiom

“…Thakur and Singh extended this definition to L-topological spaces (L ¼ ½0; 1) [12]. In [2,[8][9][10][11], many good compactness axioms (e.g. compactness, strong compactness, semicompactness and a-compactness etc.)…”

“…Kudri and Warner[10]). Let ðX ; eÞ be a topological space, f be an L-subset in the L-ts ðX ; xðeÞÞ and p 2 prðLÞ.…”

Almost Compactness Degree on L-topology

“…In [3], it was defined in [0,1]-topological spaces by using definition VII of Lowen's compactness. In [9], it was defined in L-topological spaces by using the notion of Kudri's compactness. Moreover it also was introduced in L-fuzzy topological spaces by Chen [5] and Meng [16] et al by using the notions of F -compactness and N -compactness.…”